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I'm editing a paper and the sentence I need to fix is, "Thus, the word and its_________ appear seven times in the chapter."

The word in question is a Hebrew word meaning to "rejoice" but the noun form, with an almost identical root meaning "gladness," is part of the seven occurrences. I thought of using "cognate" but that seems to be emphasizing a word "descended from the same language" which is not the emphasis here. I need a word that describes the relationship between a verb and its noun form, e.g., "to fly" and "flight."

Derivative:

(specialized language) a form of something, such as a word, made or developed from another form:

• "Detestable" is a derivative of "detest”.

(Cambridge Dictionary)

A cognate accusative/object is a figure of speech in which the verb and object are etymologically related:

He slept a troubled sleep.
Dance a dance.
Die a peaceful death.

So there shouldn't be any problem writing:

verb x and its cognate noun

Since you're dealing with a language based on consonantal roots, “noun [derived] from the same root” would also work.

The problem with derivation alone is that it assumes that, say, the verb is historically prior to the noun, which may or may not have been the case.

You could use: nominal form, nounal form or, as you yourself suggest, noun form.

These three phrases have the required emphasis on a related-but-different-parts-of-speech link between the words, rather than one of descent or derivation.

Merriam-Webster give the following definitions:

nominal adjective ...

of, relating to, or being a noun or a word or expression taking a noun construction

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nounal adjective ...

of, relating to, or of the
nature, function, or quality of a noun

And noun can itself be used adjectivally, as it is in the linguistics terms noun phrase and noun class.

A cursory glace through Google Books search results suggests nominal form gets extensive use in linguistics texts. Two relevant examples follow:

Early Indo-European languages present a wide range of nominal constructions that convey verbal action and combine a noun and a nominal form of the verb...

Archaic Syntax in Indo-European: The Spread of Transitivity in Latin, Brigitte Bauer (2011)

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The nominal form of a transitive verb that has only the prefix mang... does not differ from the stem-word, or the word to be regarded as such...

A Grammar of Toba Batak, Herman Neubronner van der van der Tuuk (2013)

Nounal form seems to be seen more in non-linguistics texts, though it is also used in linguistics too; it may be more dated as a phrase.

Similarly, "knowledge" is a nounal form rooted in verbs: OE "cnawan" meaning "to know," and OE "-cennan" meaning "To make known."

Libri, vol. 38, Jean Anker (1988)

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In these the Latin gerund is reproduced in 17 cases by a nounal form; 10 cases by a participle; 2 cases by an infinitive. The Gospels have little to teach: only one Latin gerund in the ablative has an object; this construction is paraphrased.

Publications of the Modern Language Association of America (1900)

Noun form seems to get the most general use. It's favoured in ESL circles and is also commonly used in linguistics as well.

Noun form of verb (gerund)

[For example] Rotting: When looking after food, it is important to minimise rotting.

Advanced Grammar: For Academic Writing, Richard Stevenson (2010)

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You pronounce the noun form of affect differently from the verb form. With the noun form, you stress the first syllable, and the a sounds like it would if you were saying “at.”

Grammar Essentials For Dummies, Geraldine Woods (2010)

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Even though the intrusion error in (11) is also homophonous with the target verb form, it is not itself a verb form but a noun form.

Morphological Structure in Language Processing, R. Harald Baayen, ‎Robert Schreuder (2011)

According to Google Ngram viewer, noun form also seems to be the most common of the three, with nominal form also well established and nounal form comparatively rare:

Both noun form and nominal form seem current and readily understandable, though neither is specific in describing the verb-noun relationship you require - they are, of course, more general phrases with other uses. However, your context makes the intended meaning very clear.

For what it's worth, to my mind, noun form is the nicest - it's simple and straightforward. It's also exactly the words that came to your own mind when trying to find a term!

Absent a more specific term for Semitic languages in general or Hebrew in particular (ask on Linguistics, perhaps, if that's what you want), I'd go for noun form.

To clarify the link you're trying to make, I'd also use verb rather than word, and state which noun form you are referring to, as there are possibly several different nouns related to the verb. Thus, your sentence would read:

Thus, the verb and its noun form, X, appear seven times in the chapter.

I also doubt there is a specific technical term for what you're asking for because it's not that well defined an idea, as you can see when you generalise it beyond the case at hand.

I'm not sure that the relationship between fly and flight is fundamentally the same as that between enjoy and joy, gladden and gladness, or fish (the verb) and fish (the noun) - or fishing, for that matter.

Also with enjoy, for instance, putting enjoyment and joy aside, we can conjugate two verbal nouns, enjoying and to enjoy, the to-infinitive form and the gerund: while it is Hebrew rather than English in your example, I assume there are equivalent regularly-formed verbal nouns of some sort: should they be be excluded from the term you seek? (Apologies for the laborious explanation! I'm just trying to illustrate that it's not a simple, straightforward category you seek a label for, at least as I see it.)

I minored in linguistics and I'm not aware of a single word that means "a word that shares a root with another word".

As I read the question, neither of the two words you want to describe is itself the root (if Hebrew roots work like Arabic roots and they aren't words you can say by themselves, this makes sense). So if you want to use "derivative", you would have to get a little wordier and say "Thus, these two derivatives of [root] appear seven times in the chapter."

Or just take the casual approach and say "thus, rejoice and the related word joy appear seven times", if the exact relationship between the two isn't important. I'm not sure "related word" has a formal definition as a phrase, but it sounds perfectly natural to me just based on the meaning of "related" and "word" put together.

I also like tmgr's suggestion:

Thus, the verb and its noun form, X, appear seven times in the chapter.

You have the "stem", "root", or "morpheme", or "radical", partly depending on what area of linguistics you are in [radix= latin word for (plant) root]. From one word you get a "derivative" word, and its reverse is the "primitive" form.

https://en.wikipedia.org/wiki/Word_stem

But what you are considering are inflections of a stem, https://quirkycase.wordpress.com/2013/04/17/linguistics-for-laypeople-inflection-vs-derivation/ .

deverbal noun

(e.g. destruction, container, growth and adjustment are deverbal nouns that derive from destroy, contain grow and adjust respectively)

(also, deverbal nouns are a specific subclass of derivatives, a term correctly suggested by @user240918)

Some useful references:

- Wikipedia article (general overview)

- Chomsky, Noam (1970) Remarks on Nominalization (classic discussion of the topic in Generative Grammar)

- Gurevich, Olga et al. (2008) Deverbal Nouns in Knowledge Representation (state-of-the art computational treatment of deverbal nouns)

- Grimshaw, Jane (1990) Argument Structure (chapter 4 on arguments of "event nominals")

- Marantz, Alex (1990) No Escape from Syntax: Don't Try Morphological Analysis in the Privacy of Your Own Lexicon (on deverbal nouns in a framework called "Distributed Morphology")